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Ruppeiner geometry of isotropic Blume–Emery–Griffiths model

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Abstract

With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar (m) and quadrupolar (q) order parameters, we derive an expression for the Ricci scalar (R) in the isotropic Blume–Emery–Griffiths model. Temperature dependence of R is investigated for various values of bilinear to biquadratic ratio (r). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions, there are field-dependent broad extrema in the Ricci scalar.

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Acknowledgements

We would like to thank Prof. G. Ruppeiner (New College of Florida, USA) for useful discussions related to the topic.

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Authors and Affiliations

  1. Department of Physics, Akdeniz University, Antalya, 07058, Turkey

    Rıza Erdem

  2. Institute of Science, Akdeniz University, Antalya, 07058, Turkey

    Nigar Alata

  3. Food Safety and Agricultural Research Centre, Akdeniz University, Antalya, 07058, Turkey

    Nigar Alata

Authors
  1. Rıza Erdem
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  2. Nigar Alata
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Correspondence to Rıza Erdem.

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Erdem, R., Alata, N. Ruppeiner geometry of isotropic Blume–Emery–Griffiths model. Eur. Phys. J. Plus 135, 911 (2020). https://doi.org/10.1140/epjp/s13360-020-00934-3

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00934-3

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